In an election between two candidates A and B, the number of valid votes…
2023
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did B get ?
- A.
4142
- B.
2834
- C.
2420
- D.
3150
Attempted by 32 students.
Show answer & explanation
Correct answer: B
Answer: 2834
Compute total valid votes: 80% of 8720 = 0.8 × 8720 = 6976.
Compute the difference between votes for the two candidates: 15% of total polled = 0.15 × 8720 = 1308, so a − b = 1308.
Set up the system: a + b = 6976 and a − b = 1308.
Solve: adding the equations gives 2a = 6976 + 1308 = 8284, so a = 4142. Then b = 6976 − 4142 = 2834.
Therefore the number of valid votes received by candidate B is 2834.